Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it int
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Solve the following problem for the roots by using the quadratic formula.
2(6 - x) = x(x + 5)

Answer:

times 4 or multiply by 4each time

Answer:

D. 5 tan ø

Step-by-step explanation:

[tex]5 \sin \phi \: \sec \phi \\ \\ = 5 \sin \phi \: \times \frac{1}{ \cos \phi} \\ \\ = 5 \frac{\sin \phi}{ \cos \phi} \\ \\ = 5 \tan \phi[/tex]

Answer:

Correct choice D.

Step-by-step explanation:

Trigonometric Identities

We need to recall some properties and definitions of the trigonometric functions.

[tex]\tan \theta=\frac{\sin\theta}{\cos\theta}[/tex]

[tex]\sec \theta=\frac{1}{\cos\theta}[/tex]

It's required to simplify the following expression:

[tex]5\sin\theta\sec\theta[/tex]

Substituting the identity for the secant:

[tex]\displaystyle 5\sin\theta\sec\theta=5\sin\theta.\frac{1}{\cos\theta}[/tex]

Operating:

[tex]\displaystyle 5\sin\theta\sec\theta=5\frac{\sin\theta}{\cos\theta}[/tex]

Now we use the definition of the tangent:

[tex]\displaystyle 5\sin\theta\sec\theta=5\tan\theta[/tex]

Correct choice D.

Step-by-step explanation:

Hey there!

Given eqautions are:

y = 2x + 1......... (i)

y = 4x - 3...........(ii)

Putting eqaution (ii) in eqaution (i), we get;

4x - 3 = 2x + 1

~ Keep like terms on same side.

4x - 2x = 1+3

~ Perform operations. ( +, -, *, /)

2x = 4

x= 4/2

Therefore, X= 2.

Putting the value of X in eqaution (i)

y = 2x+1

y = 2*2+1

Therefore, y= 5.

Therefore, the ordered pair is (2,5).

Hope it helps...

Which of the following ordered pairs are solutions to the system of equations below? y = 2x + 1 and y = 4x – 3 (1,4) (4,5) (2,5) (3,7)

Step-by-step explanation:

Hey there!

Given eqautions are:

y = 2x + 1......... (i)

y = 4x - 3...........(ii)

Putting eqaution (ii) in eqaution (i), we get;

4x - 3 = 2x + 1

~ Keep like terms on same side.

4x - 2x = 1+3

~ Perform operations. ( +, -, *, /)

2x = 4

x= 4/2

Therefore, X= 2.

Putting the value of X in eqaution (i)

y = 2x+1

y = 2*2+1

Therefore, y= 5.

Therefore, the ordered pair is (2,5).

Hope it helps...

Answer:

put a circle, *fill it in, on -9

then, make it pointed towards the right

Step-by-step explanation:

Answer:

What are you asking

Step-by-step explanation:

Answer:

h(-6) = -4

Step-by-step explanation:

just plug in -6 where you see "x" and you get

3(-6) -2 / 5 and you get

multiply

-18 -2 / 5

subtract

-20 / 5

your final answer is

h(-6) = -4

Answer:

An unknown variable

Step-by-step explanation:

r is an unknown variable -> the equation is used to solve for it.

Answer:

In math, r usually stands for radius.

Step-by-step explanation:

Answer:

Step-by-step explanation:

1) The function f(x) = x is a straight line rising to the right and passing through the origin at an angle of 45 degrees This means this it passes though the points  .....   (-2, -2),  (-1, -1),  (1, 1),  (2, 2) .......

If g(x) = f(x) + 4 then g(x) will be a straight line parallel to f(x) where each point on g(x) is   4 units vertically up from each point on f(x). Its a translation of f(x) up 4 units.

The slope of both graphs is 1.

2) This line (g)x passes through the origin but has slope 1/3.

Answer:

I don’t know 160.

Step-by-step explanation:

20 plus 160 equals 180.

The correct answer is 20° since x and 20° are vertically opposite angles.

In other words, the value of x is equal to 20°.

Vertically opposite angles are formed by the intersection of two lines. They are opposite each other and have equal measures. When two lines intersect, the vertically opposite angles are formed on the opposite sides of the intersection point. These angles are also known as vertical angles or opposite angles. The property of vertical angles states that their measures are equal. This means that if one angle measures x degrees, the other vertical angle will also measure x degrees. Vertically opposite angles are important in geometry and are often used to prove theorems and solve geometric problems.

Therefore, the correct answer is 20° since x and 20° are vertically opposite angles.In other words, the value of x is equal to 20°.

Learn more about vertically opposite angles here:

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Answer:

c = 196

Step-by-step explanation:

To obtain a perfect square trinomial

Add ( half the coefficient of the x- term )² to x² + 28x

x² + 2(14)x + (14)², that is

x² + 28x + 196

= (x + 14)² ← a perfect square

Answer:

c = 196

Step-by-step explanation:

28 /2 = 14

14 x 14 = 196

formula =( b/2) x 2

Answer:

Step-by-step explanation:

Step-by-step explanation:

This is a case of conditional probability, in which we have to find the probability of ocurance of event E when when event F has already ocured.

To find the probability of at least one of something, calculate the probability of none and then subtract that result from 1.

That is, P(at least one) = 1 – P(none)

Given:

Seeds planted = [tex]1\dfrac{2}{3}[/tex] rows

Crows ate = [tex]1\dfrac{1}{5}[/tex] rows

To find:

The remaining rows of seeds.

Solution:

According to the question,

Remaining rows of seeds = Seeds planted - Crows ate

                                          [tex]=1\dfrac{2}{3}-1\dfrac{1}{5}[/tex]

                                          [tex]=\dfrac{1(3)+2}{3}-\dfrac{1(5)+1}{5}[/tex]

                                          [tex]=\dfrac{3+2}{3}-\dfrac{5+1}{5}[/tex]

                                          [tex]=\dfrac{5}{3}-\dfrac{6}{5}[/tex]

Taking LCM, we get

[tex]=\dfrac{5(5)-3(6)}{15}[/tex]

[tex]=\dfrac{25-18}{15}[/tex]

[tex]=\dfrac{7}{15}[/tex]

Therefore, [tex]\dfrac{7}{15}[/tex] rows of seeds are left.

Answer:

[tex]\frac{x+9}{x+3}[/tex] , x ≠ - 3 ;

Step-by-step explanation:

f(x) = x³ + 9x² - 25x - 225 = (x + 9)(x + 5)(x - 5)

g(x) = x³ + 3x² - 25x - 75 = (x + 5)(x + 3)(x - 5)

( [tex]\frac{f}{g}[/tex] )(x) = [tex]\frac{(x+9)(x+5)(x-5)}{(x +5)(x+3)(x-5)}[/tex] = [tex]\frac{x+9}{x+3}[/tex] , x ≠ - 3

652.50

Step-by-step explanation:

1450 x .09 x 5 = 652.50

Answer:(a)

Step-by-step explanation:

Answer:

80 cubic units

Step-by-step explanation:

Volume of rectangular pyramid = ⅓*L*W*H

L = 8 units

W = 5 units

H = OP = 6 units

Plug in the values into the equation

Volume = ⅓*8*5*6

Volume = 80 cubic units

Answer:

(0,3)

Step-by-step explanation:

the x intercept is where the line crosses x which is at (0,3)

Answer:

i think it's 0, 3 for the answer

Answer:

Surface area of rectangular prism = 1550m²

Surface area of triangular prism = 498m²

Step-by-step explanation:

The surface area of a rectangular prism is given by the formula

A= 2(wl+hl+hw)

Where A = surface area

w= width

l= length

h=height

Given that the rectangular prism has a length of 15 meters, width of 10 meters, and height of 25 meters.

A= 2(10×15+25×15+25×10)

A=2(150+375+250)

A=2(775)

A=1550 square meters

Surface area of triangular prism = base of triangle x height of triangle + (length of rectangle x width of rectangle) x 3

Since we are not given length and width of the triangular prism, we could assume the triangular prism has same length and width with the rectangular prism given that it is a composite shape(more than one solid in one)

Given triangular base with a base of 6 meters and height of 8 meters.

Surface area of triangular prism= 6×8+(10×15)×3

=48+150×3

=48+450

= 498 square meters

Surface area of a solid is the 2 dimensional space its surface covers. The surface area of the considered composite solid is given by: Option B: 1658 sq. meters

Composite figure is figure made by composing two or more figure. The composite figure may leave a surface common as not a surface of the resultant composite figure due to it being the joining area of two figures, thus, not remaining a surface.

Thus, its surface area would sum of their surface areas - areas of those regions which are not surface anymore.

For the given case, the prisms given are having surface areas as:

Composite figure's surface area = Surface area of its composing figures - any overlapping areas

Surface area of rectangular prism  = [tex]2(L.W + W.H + H.L) = 2(15 \times 10 + 10 \times 25 + 25 \times 15) = 1550[/tex] sq. meters.

Surface area of triangular prism = area of its three rectangular faces + area of its base triangles.

For the triangle ABI, Pythagoras theorem is proved to be true with angle I (internally) being right angled triangle. (As we have [tex]10^2 = 8^2 + 6^2[/tex] )

That means the area of those triangles would be base times height times half, which comes as [tex]8 \times 6 \time 1/2 = 24[/tex] sq. units.

The three faces have area as= [tex]15 \times 10 + 15 \times 6 + 15 \times 8 = 15(24) = 360[/tex] sq. meters.

Sum of area of triangular prism and rectangular prism is 1550 + 408 = 1958 sq. meters

Thus, the surface area of the considered composite solid is given by: Option B: 1658 sq. meters

Learn more about surface area here:

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Answer:

is there anymore info in it

Step-by-step explanation:

Step-by-step explanation:

We are finding a polynomial of degree 3.

Since 4 and 5i are the zeroes of the polynomial,

the conjugate -5i must also be such a zero.

=> f(x) = a(x - 4)(x - 5i)(x + 5i)

=> f(x) = a(x - 4)(x² - 25i²)

=> f(x) = a(x - 4)(x² + 25)

When x = 1, f(1) = -234.

=> a(1 - 4)(1² + 25) = -234

=> a(-3)(-26) = -234

=> -78a = -234

=> a = 3

Hence,

f(x) = 3(x - 4)(x² + 25) = 3x³ - 12x² + 75x - 300.

Answer:

Equivalent fractions

3/10 = 6/20

1/4 = 5/20

4/5 = 16/20

Step-by-step explanation:

For

3/10

We Multiply numerator and Denominator by 2

= 3×2/10 × 2

= 6/20

For 1/4

We Multiply numerator and Denominator by 5

= 1×5/4× 5

= 5/20

For 4/5

We Multiply numerator and Denominator by 4

= 4×4/5× 4

4/5 = 16/20

Given:

The two shapes P and Q on a coordinate plan.

To find:

(a) The area of shape P.

(b) Mathematical name of quadrilateral Q.

Solution:

(a)

From the given figure, it is clear that shape P is a triangle.

Area of a triangle is

[tex]A=\dfrac{1}{2}\times Base\times Height[/tex]

Area of triangle P whose base is 4 and height is 6, is

[tex]A=\dfrac{1}{2}\times 4\times 6[/tex]

[tex]A=\dfrac{24}{2}[/tex]

[tex]A=12[/tex]

So, the area of shape P is 12 sq. units.

(b)

In quadrilateral Q, two pairs of congruent sides are adjacent to each other.

So, Q is a kite.

Therefore, the mathematical name of quadrilateral Q is kite.

Answer:

Step-by-step explanation:

Given:

The two shapes P and Q on a coordinate plan.

To find:

(a) The area of shape P.

(b) Mathematical name of quadrilateral Q.

Solution:

(a)

From the given figure, it is clear that shape P is a triangle.

Area of a triangle is

Area of triangle P whose base is 4 and height is 6, is

So, the area of shape P is 12 sq. units.

(b)

In quadrilateral Q, two pairs of congruent sides are adjacent to each other.

So, Q is a kite.

Therefore, the mathematical name of quadrilateral Q is kite.

Answer:

1/3

Step-by-step explanation:

-4/15+3/5

-4/15+3×3/5×3

-4/15+9/15

-4+9/15

5/15

1/3

Hope this helps!

Answer:

1/3

Step-by-step explanation:

-4/15+3/5

-4/15+3×3/5×3

-4/15+9/15

-4+9/15

5/15

1/3

Answer:

$ 13.80

Step-by-step explanation:

Answer:

Hope this helps!

Step-by-step explanation:

Answer -Full amonut - $13.80. Tip amount - $1.80

First, convert the 15% to an actual number that can be used in a calculation. For percents, this is always done by simply dividing the percent (in this case 15%) by 100%.So, the conversational term "15%" becomes 15% / 100% = 0.15 in terms of a real mathematical number.

Second, you need to find out what 15% of your $12 meal cost is. This is always done by multiplying 0.15 by $12.00, or

0.15 x $12.00=$1.80.

So, the amount of tip you are going to leave is $1.80. full amount - 13.80

Answer:

The answer is 180 degrees.

Step-by-step explanation:

The rotation that maps one side to an adjacent side is 360°/6 = 60°. This is the least rotation that plots the regular hexagon to the aforementioned. In the least whole number of these minimum rotations, such as three 60° rotations to make 180°, will retain the hexagon identical.

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Answer:

n=22

Step-by-step explanation:

(x^4)(x^3)^6=x^n

x^4*x^18=x^n

since the bases are the same, then equate the powers.

4+18=n

n=22